Stopping rules for phase II studies

This paper, the second in a series of three papers concerned with the statistical aspects of interim analyses in clinical trials, is concerned with stopping rules in phase II clinical trials. Phase II trials are generally small-scale studies, and may include one or more experimental treatments with or without a control. A common feature is that the results primarily determine the course of further clinical evaluation of a treatment rather than providing definitive evidence of treatment efficacy. This means that there is more flexibility available in the design and analysis of such studies than in phase III trials. This has led to a range of different approaches being taken to the statistical design of stopping rules for such trials. This paper briefly describes and compares the different approaches. In most cases the stopping rules can be described and implemented easily without knowledge of the detailed statistical and computational methods used to obtain the rules.

Interim analyses and sequential designs in phase III studies

Recruitment of patients to a clinical trial usually occurs over a period of time, resulting in the steady accumulation of data throughout the trial's duration. Yet, according to traditional statistical methods, the sample size of the trial should be determined in advance, and data collected on all subjects before analysis proceeds. For ethical and economic reasons, the technique of sequential testing has been developed to enable the examination of data at a series of interim analyses. The aim is to stop recruitment to the study as soon as there is sufficient evidence to reach a firm conclusion. In this paper we present the advantages and disadvantages of conducting interim analyses in phase III clinical trials, together with the key steps to enable the successful implementation of sequential methods in this setting. Examples are given of completed trials, which have been carried out sequentially, and references to relevant literature and software are provided.

Autosomal dominant peripheral cystic retinal patches and non-cystic retinal tufts associated with peripapillary crescents, retinal breaks and uveitis

PURPOSE

To characterise an Irish kindred with apparent autosomal dominant peripheral retinal lesions and peripapillary crescents associated with retinal breaks and uveitis and assess whether these findings were associated with altered homocysteine metabolism.

METHODS

Family members were followed prospectively and regularly examined. Molecular genetic analysis was performed on family members to detect cystathionine beta-synthase (CBS) 307G-S and 5,10-methylenetetrahydrofolate (MTHFR) 677C-T mutations.

RESULTS

Over 11 years, 25 family members in four generations were examined, none of whom had significant refractive errors. Fifteen affected individuals had peripheral cystic retinal patches and in some cases non-cystic retinal tufts, associated with peripapillary pigmentation. Mean age at first examination of affected and non-affected individuals was the same. During follow-up the fundal findings remained unchanged in the affected group and no clinical characteristics developed in the unaffected individuals. Two affected siblings had associated uveitis and rhegmatogenous retinal detachment, which were successfully treated, while a third affected individual had a pigmented retinal break not requiring treatment. Heterozygosity for the CBS 307G-S mutation did not segregate with affected individuals while the MTHFR 677C-T mutation was not detected.

CONCLUSIONS

This family has previously undescribed fundal findings inherited in an apparent autosomal dominant pattern associated with retinal breaks and uveitis. There is no associated inherited alteration of homocysteine metabolism.

Mid-trial design reviews for sequential clinical trials

When sequential clinical trials are conducted by plotting a statistic measuring treatment difference against another measuring information, power is guaranteed regardless of nuisance parameters. However, values need to be assigned to nuisance parameters in order to gain an impression of the sample size distribution. Each interim analysis provides an opportunity to re-evaluate the relationship between sample size and information. In this paper we discuss such mid-trial design reviews. In the special cases of trials with a relatively short recruitment phase followed by a longer period of follow-up, and of normally distributed responses, mid-trial design reviews are particularly important. Examples are given of the various situations considered, and extensive simulations are reported demonstrating the validity of the review procedure in the case of normally distributed responses.

Diltiazem in acute myocardial infarction treated with thrombolytic agents: a randomised placebo-controlled trial. Incomplete Infarction Trial of European Research Collaborators Evaluating Prognosis post-Thrombolysis (INTERCEPT)

BACKGROUND

Diltiazem reduces non-fatal reinfarction and refractory ischaemia after non-Q-wave myocardial infarction, an acute coronary syndrome similar to the incomplete infarction that occurs after successful reperfusion. We postulated that this agent would reduce cardiac events in patients after acute myocardial infarction treated initially with thrombolytic agents-a clinical application previously unexplored with heart-rate-lowering calcium antagonists.

METHODS

A prospective, randomised, double-blind, sequential trial was done in 874 patients with acute myocardial infarction, but without congestive heart failure, who first received thrombolytic agents. Patients received either 300 mg oral diltiazem once daily, or placebo, initiated within 36-96 h of infarct onset, and given for up to 6 months. The trial primary endpoint was the cumulative first event rate of cardiac death, non-fatal reinfarction, or refractory ischaemia. Additional prespecified endpoints included several composites of non-fatal cardiac events (non-fatal reinfarction combined with refractory ischaemia, all recurrent ischaemia, or the need for myocardial revascularisation). The diagnosis of ischaemia, whether refractory or recurrent, and the need for myocardial revascularisation, was always based on objective electrocardiographical evidence of ischaemia, either at rest or on exertion.

RESULTS

For the trial primary endpoint, 131 events occurred in the 444 placebo patients and 97 events in the 430 diltiazem patients (hazard ratio 0.79; 95% CI, 0.61-1.02; p=0.07). For non-fatal cardiac events, diltiazem treatment was associated with a relative decrease (0.76; 0.58-1.00) in the combined event rate of non-fatal reinfarction and refractory ischaemia. There was a similar decrease in the composite non-fatal endpoints of non-fatal reinfarction combined with all recurrent ischaemia (0.80; 0.64-1.00) and non-fatal reinfarction combined with the need for myocardial revascularisation (0.67; 0.46-0.96). The need for myocardial revascularisation alone was significantly reduced by 42% (0.61; 0.39-0.96). No major safety issues were encountered.

CONCLUSIONS

Diltiazem did not reduce the cumulative occurrence of cardiac death, non-fatal reinfarction, or refractory ischaemia during a 6-month follow-up, but did reduce all composite endpoints of non-fatal cardiac events, especially the need for myocardial revascularisation.

Tolerance and rebound insomnia with rapidly eliminated hypnotics: a meta-analysis of sleep laboratory studies

Differences in development of tolerance and occurrence of rebound insomnia have been well established between rapidly and slowly eliminated benzodiazepine hypnotics. Based on meta-analytic methodology, this study assesses whether there are such differences among the rapidly eliminated benzodiazepine and benzodiazepine-like hypnotics (brotizolam, midazolam, triazolam, zolpidem and zopiclone). All sleep laboratory studies of these drugs (n = 137) published from 1966 to 1997 were obtained, mainly through a MEDLINE search. Rigorous selection criteria resulted in the inclusion of 75 studies employing 1276 individuals (804 insomniacs and 472 healthy volunteers). Using a mixed effects regression model, reliable estimation of the effects on insomniacs of the recommended dose of each drug could be obtained. All five rapidly eliminated hypnotics showed statistically significant initial efficacy. Tolerance with intermediate and long-term use was clearly developed with triazolam and was only marginal with midazolam and zolpidem; it could not be estimated for brotizolam or zopiclone because of insufficient data. Rebound insomnia on the first withdrawal night was intense with triazolam and mild with zolpidem; data were unavailable for brotizolam and inadequate for midazolam and zopiclone. In conclusion, there are differences among the rapidly eliminated hypnotics with respect to tolerance and rebound insomnia suggesting that, in addition to short elimination half-life, other pharmacological properties are implicated in the mechanisms underlying these side-effects.

Combining summaries of binary outcomes with those of continuous outcomes in a meta-analysis

We present a methodology for combining trials some of which report continuous outcome measures and others binary outcomes created by a dichotomy of the continuous measurement. This was motivated by a series of controlled clinical trials investigating the effect of prophylactic use of oxytocics on postpartum blood loss during labor. Data were available in the form of summary statistics from published papers. The log-odds ratio is used as a common measure of treatment difference across all trials. We discuss the general applicability of this approach.

Cholinesterase inhibition for Alzheimer disease: a meta-analysis of the tacrine trials. Dementia Trialists' Collaboration

OBJECTIVES

To determine the effects of cholinesterase inhibition with tacrine hydrochloride for the symptoms of Alzheimer disease in terms of cognitive performance, clinical global impression, behavior, and functional autonomy.

DATA SOURCES

The Cochrane Dementia Group registry of trials.

STUDY SELECTION

Unconfounded, randomized, double-blind, placebo-controlled trials in which tacrine had been given for more than 1 day and that were completed before January 1, 1996.

DATA EXTRACTION

Two reviewers independently selected trials for inclusion and individual patient data were sought.

DATA SYNTHESIS

Data were analyzed from 12 trials that included 1984 patients with Alzheimer disease. At 12 weeks, cognitive performance, as measured by the Mini-Mental State Examination (score range, 0-30), was better in patients receiving tacrine than in patients receiving placebo by 0.62 points (95% confidence interval [CI], 0.23-1.00; P=.002). Compared with similar untreated patients who would be expected to deteriorate by 0.50 to 1.00 points on the Mini-Mental State Examination during 12 weeks, the progress of patients receiving tacrine would be expected to range between an improvement of 0.12 and a deterioration of 0.38 points. The odds ratio for improvement on the Clinical Global Impression of Change scale (range, 1-7) for patients receiving tacrine compared with those receiving placebo was 1.58 (95% CI, 1.18-2.11; P=.002). The behavioral noncognitive subscale of the Alzheimer's Disease Assessment Scale (range, 0-50) showed a difference in favor of tacrine of 0.58 points (95% CI, 0.17-1.00; P= .006). Improvement on the Progressive Deterioration Scale, largely an index of functional activities, was not significant (0.75; 95% CI, -0.43 to 1.93; P=.21). Age, severity of dementia, and exposure to tacrine prior to randomization had no clear influence on the treatment effect. There was a nonsignificant trend toward increasing effect with increasing dose for cognitive function and the Clinical Global Impression of Change. For patients without prior exposure to tacrine, the odds of patients' withdrawing during the study while they were receiving tacrine compared with placebo was 3.63 (95% CI, 2.80- 4.71; P<.001). Eleven (95% CI, 7-31) patients would need to be treated to achieve any improvement on the Clinical Global Impression scale, and 42 (95% CI, 23-125) to achieve a moderate or marked improvement. One patient would be expected to withdraw for every 4 (95% CI, 3-5) patients treated.

CONCLUSIONS

Cholinesterase inhibition with tacrine appears to reduce deterioration in cognitive performance during the first 3 months and increase the odds of global clinical improvement. Effects observed on measures of behavioral disturbance were of questionable clinical significance, and functional autonomy was not significantly affected. The clinical relevance of the benefits of cholinesterase inhibition remains controversial, and long-term trials with clinically relevant end points are required.

Randomised controlled trial of laparoscopic versus open mesh repair for inguinal hernia: outcome and cost

OBJECTIVE

To compare tension-free open mesh hernioplasty under local anaesthetic with transabdominal preperitoneal laparoscopic hernia repair under general anaesthetic.

DESIGN

A randomised controlled trial of 403 patients with inguinal hernias.

SETTING

Two acute general hospitals in London between May 1995 and December 1996.

SUBJECTS

400 patients with a diagnosis of groin hernia, 200 in each group.

MAIN OUTCOME MEASURES

Time until discharge, postoperative pain, and complications; patients' perceived health (SF-36), duration of convalescence, and patients' satisfaction with surgery; and health service costs.

RESULTS

More patients in the open group (96%) than in the laparoscopic group (89%) were discharged on the same day as the operation (chi2 = 6.7; 1 df; P=0.01). Although pain scores were lower in the open group while the effect of the local anaesthetic persisted (proportional odds ratio at 2 hours 3.5 (2.3 to 5.1)), scores after open repair were significantly higher for each day of the first week (0.5 (0.3 to 0.7) on day 7) and during the second week (0.7 (0.5 to 0.9)). At 1 month there was a greater improvement (or less deterioration) in mean SF-36 scores over baseline in the laparoscopic group compared with the open group on seven of eight dimensions, reaching significance on five. For every activity considered the median time until return to normal was significantly shorter for the laparoscopic group. Patients randomised to laparoscopic repair were more satisfied with surgery at 1 month and 3 months after surgery. The mean cost per patient of laparoscopic repair was 335 pounds (95% confidence interval 228 pounds to 441 pounds) more than the cost of open repair.

CONCLUSION

This study confirms that laparoscopic hernia repair has considerable short term clinical advantages after discharge compared with open mesh hernioplasty, although it was more expensive.

A prospectively planned cumulative meta-analysis applied to a series of concurrent clinical trials

Sequential designs are now a familiar part of clinical trial methodology. In particular, the triangular test has been used in several individual studies. Methods of combining studies are also well-known from the literature on meta-analysis. However, the combination of the two approaches is new. Consider the situation where a series of studies is to be conducted, following broadly similar protocols comparing a new treatment with a control treatment. In order to obtain an answer as quickly as possible to an efficacy or safety question it may be desirable to perform a cumulative meta-analysis on one particular variable. This could, for example, be the primary efficacy variable, an expensive assessment conducted in only a subgroup of patients, or a serious side-effect. To allow for the size of the treatment difference varying from study to study we might wish to provide a global estimate. Hence a random effects combined analysis, within a sequential framework, would appear to be appropriate. A methodology which utilizes efficient score statistics and Fisher's information is presented. Simulations show that the proposed methodology will achieve the specified error probabilities with reasonable accuracy provided that any random effect is relatively small. Ignoring random effects when they are present can lead to inaccuracies. A simulated example illustrates a number of practical issues.

Borrowing strength from external trials in a meta-analysis

There exists a variety of situations in which a random effects meta-analysis might be undertaken using a small number of clinical trials. A problem associated with small meta-analyses is estimating the heterogeneity between trials. To overcome this problem, information from other related studies may be incorporated into the meta-analysis. A Bayesian approach to this problem is presented using data from previous meta-analyses in the same therapeutic area to formulate a prior distribution for the heterogeneity. The treatment difference parameters are given non-informative priors. Further, related trials which compare one or other of the treatments of interest with a common third treatment are included in the model to improve inference on both the heterogeneity and the treatment difference. Two approaches to estimating relative efficacy are considered, namely a general parametric approach and a method explicit to binary data. The methodology is illustrated using data from 26 clinical trials which investigate the prevention of cirrhosis using beta-blockers and sclerotherapy. Both sources of external information lead to more precise posterior distributions for all parameters, in particular that representing heterogeneity.

Borrowing strength from external trials in a meta-analysis

There exists a variety of situations in which a random effects meta-analysis might be undertaken using a small number of clinical trials. A problem associated with small meta-analyses is estimating the heterogeneity between trials. To overcome this problem, information from other related studies may be incorporated into the meta-analysis. A Bayesian approach to this problem is presented using data from previous meta-analyses in the same therapeutic area to formulate a prior distribution for the heterogeneity. The treatment difference parameters are given non-informative priors. Further, related trials which compare one or other of the treatments of interest with a common third treatment are included in the model to improve inference on both the heterogeneity and the treatment difference. Two approaches to estimating relative efficacy are considered, namely a general parametric approach and a method explicit to binary data. The methodology is illustrated using data from 26 clinical trials which investigate the prevention of cirrhosis using beta-blockers and sclerotherapy. Both sources of external information lead to more precise posterior distributions for all parameters, in particular that representing heterogeneity.

An alternative approach to the analysis of animal carcinogenicity studies

Long-term animal carcinogenicity studies are an important part of the risk analysis process assessing the carcinogenic potential of products to humans. Results from the statistical analysis of the data from such studies are generally presented as a series of hypothesis tests indicating whether there was a significant rise in the number of tumors at given sites. The conclusion from such an analysis depends on the size of the experiment. In particular, the number of false-negative results can be high when tumors are rare. In this paper, a test for equivalence fixing the proportion of false negatives is proposed. The effect on the required sample size is also discussed.

The fixed-dose procedure and the acute-toxic-class method: a mathematical comparison

The fixed-dose procedure (FDP), proposed by the British Toxicology Society, and the acute-toxic-class (ATC) method, proposed by the German Federal Health Authority, provide alternatives to the LD50 test for classifying substances by their acute oral toxicity. This paper presents a mathematical model that is used to compare the two procedures in terms of their classification properties and the required numbers of animals. It is found that the classification properties of the procedures depend on the dose levels used, the number of animals tested per dose and the criteria that are used to decide whether testing should continue at a higher or lower dose. For substances with steep dose-response curves, the most likely classification is determined chiefly by the choice of the dose levels whilst the number of animals and continuation criteria used are increasingly important for substances with dose-response curves with a smaller slope. The use of toxicity as a possible endpoint as in the FDP and the use of a two-stage testing procedure at each dose as in the ATC method are both found to reduce the expected numbers of animals required with little effect on the classification properties. On the strength of these findings it is indicated that a new procedure combining the dose levels and testing approach of the ATC method with the inclusion of toxicity as an endpoint as in the FDP would be more efficient than either the FDP or the ATC method.

Estimating the magnitude of carcinogenic effects in long-term animal studies

Carcinogenicity studies seek to compare the incidence of tumours in animals exposed to the substance under investigation and animals used as controls. The conventional method of analysis is the Peto test, which assumes that tumours are either instantly fatal or have no effect on mortality and requires a judgement to be made regarding the lethality of each tumour. Such an assumption seems unrealistic and the judgement is often difficult to make and unreliable. The need for such a judgement and the assumption of extreme lethality can be removed by using parametric multi-state models. In this modelling approach the transition of animals between the states 'alive without a tumour', 'alive with a tumour' and 'dead' is modelled mathematically. This paper compares the Peto test with tests based on two parametric multi-state models in terms of the sensitivity of the tests to detect carcinogenicity. The sensitivity, or power, is shown to be low for commonly used numbers of animals, depending chiefly on the expected total number of animals with tumours. The Omar and Whitehead multi-state model is found to be slightly more powerful than the Dewanji et al. model and at least as powerful as the Peto test. Provided the parametric assumptions are appropriate, this method thus gives a test that is more sensitive than the Peto test and enables estimation of tumour onset and mortality rates without the requirement of tumour lethality judgements.

Design of a placebo-controlled clinical trial of long-acting diltiazem and aspirin versus aspirin alone in patients receiving thrombolysis with a first acute myocardial infarction. Incomplete Infarction Trial of European Research Collaborators Evaluating Prognosis Post-Thrombolysis (diltiazem) (INTERCEPT) Research Group

Several pharmacologic forms of adjunctive therapy, designed to enhance the efficacy of thrombolysis following acute myocardial infarction (AMI), are being explored. However, few studies have assessed the use of standard secondary prevention therapies (beta-blockers, angiotensin-converting enzyme inhibitors, magnesium, calcium antagonists, etc.) for antecedent thrombolysis. Although calcium antagonists have not been shown to alter post-AMI mortality, diltiazem has been shown to reduce recurrent nonfatal infarction and myocardial ischemia following non-Q-wave AMI. Because both non-Q-wave AMI and AMI treated with thrombolytic therapy result in early reperfusion and clinical manifestations of "incomplete infarction" (i.e., aborted transmural infarction), we hypothesize that prophylactic administration of diltiazem to AMI patients who receive thrombolysis before other therapies might decrease ischemic complications. We have initiated a multicenter, randomized, placebo-controlled, double-blind, parallel-group comparison of long-acting diltiazem 300 mg/day and aspirin 160 mg/day versus aspirin 160 mg/day alone in up to 920 patients with an uncomplicated first AMI (no heart failure or left ventricular dysfunction) within 36 to 96 hours of receiving thrombolysis. Active enrollment is under way at 46 centers in the United Kingdom, Belgium, The Netherlands, and Denmark. This trial (known as the Incomplete INfarction Trial of European Research Collaborators Evaluating Prognosis Post-Thrombolysis [diltiazem], or INTERCEPT) represents the first long-term, large-scale, prospective study of a calcium antagonist administered post-thrombolysis as adjunctive therapy to AMI patients in which the primary trial objective is to assess the effect of blinded therapy on the 6-month cumulative occurrence of a combined clinical end point (cardiac death, recurrent nonfatal AMI, and medically refractory ischemia).

Reducing animal numbers in the fixed-dose procedure

The fixed-dose procedure (FDP) was proposed by the British Toxicology Society (1984) as an alternative to assessment of acute oral toxicity via estimation of the LD50. The procedure is incorporated in OECD guidelines on acute oral toxicity testing. Whitehead and Curnow (1992) used a mathematical model to describe the statistical properties of the FDP. This paper uses a simplified model to investigate further the procedure. In particular the effects of altering the number of animals included at each stage in the procedure are evaluated. It is shown that a reduction in the number of animals tested makes little difference to the toxic classification of a substance with a steep dose-response curve, but has increasing effect as the dose-response curve becomes shallower. The simplified model also shows that in the proposed procedure the most likely classification depends on the LD of the substance tested. Changing the number of animals tested results in the most likely classification depending on other LD values. The effect of additional variation is also considered. Such variation might arise from within-laboratory differences. Although this increases the range of substances for which misclassification is likely, the increase is not much affected by the number of animals tested.

A meta-analysis of clinical trials involving different classifications of response into ordered categories

Statistical methods are available for performing a meta-analysis when the response variable of interest is the same in each study. Problems arise when studies exploring a common therapeutic question use different patient response types. This article presents statistical methods for combining studies which involve different classifications of response into ordered categories. The assumptions required for the stratified proportional odds model, on which the analysis is based, are discussed. The approach is illustrated using results from a series of studies investigating the prevention of gastrointestinal damage induced by non-steroidal anti-inflammatory drugs.

Contamination of hands and work surfaces with Salmonella enteritidis PT4 during the preparation of egg dishes

Salmonella enteritidis PT4 was recovered from fingers following the breaking of intact shell eggs artificially contaminated in the contents with the bacterium. Kitchen utensils used to mix egg dishes were salmonella-positive, sometimes after washing. Following the preparation of batter or the mixing of eggs, S. enteritidis was recovered from work surfaces over 40 cm from the mixing bowl. The bacterium survived well in thin, dry films of either batter or egg and, from an initial level of one cell per cm2, could be recovered from formica work surfaces 24 h after contamination.

Chemical emergencies and the Health Advisory Group on Chemical Contamination Incidents (HAGCCI)

The Health Advisory Group on Chemical Contamination Incidents (HAGCCI) (pronounced 'Hag-C'), is an independent advisory group which was established to advise Directors of Public Health throughout the United Kingdom (UK) and the Chief Medical Officers of the UK Health Departments on the medical aspects of major chemical contamination incidents involving air, soil or water. Separate arrangements exist for the provision of advice on chemical contamination of food. HAGCCI comprises a core group of three individuals, supported by a multidisciplinary panel of experts, and a secretariat provided by the Department of Health. We describe the role of HAGCCI within the overall framework of preparedness for the public health aspects of chemical emergencies.

Egg age and the growth of Salmonella enteritidis PT4 in egg contents

The growth of Salmonella enteritidis PT4 in albumen around an intact yolk was governed by the age of the egg on inoculation. In the majority of eggs, held at 20 degrees C, the bacterium was unable to grow rapidly until eggs had been stored for approximately 3 weeks. The multiplication of S. enteritidis in stored eggs appeared to be associated with alterations to the yolk membrane which allowed the bacterium to either invade the yolk or obtain nutrients from it. The rate at which egg contents change to permit the growth of S. enteritidis would appear to be temperature related and took place more rapidly when eggs were stored under conditions where temperatures fluctuated and, on occasions, reached 30 degrees C.

Influence of feeding patterns on the artificial infection of laying hens with Salmonella enteritidis phage type 4

Salmonella enteritidis phage type 4 was recovered significantly more frequently from the crops of birds which had been denied food for 24 hours than from birds allowed food ad libitum. There was, however, no difference in its isolation rate from tissues. Within one hour of infection, S enteritidis could be recovered from a variety of tissues, including the oviduct, of a small proportion of the infected birds.